Police also identified the former spokesman, a close Netanyahu confidant, as someone they had arrested two days earlier in a separate case involving allegations of corruption at Israel's biggest telecoms company.
The four-term premier is faced with one of the biggest challenges to his long dominance of Israeli entity’s politics. Police recommended a week ago that he could be indicted for bribery and fraud.
He has denied wrongdoing in what are now four separate investigations, including two in which he is personally a suspect. He says the allegations are a political "witch hunt".
In the latest case, police said former Netanyahu spokesman Nir Hefetz had offered through an intermediary in 2015 to help a judge win the post of attorney general if she agreed to use the position to block any proceedings against Netanyahu's wife Sara.
Last September, Attorney-General Avichai Mandelblit said he was considering indicting Sara Netanyahu for fraud over suspected use of state funds for personal dining and catering services amounting to some $100,000. She has denied the allegations and a final decision on charges is pending.
The prime minister rejected the allegation about the attempt to bribe the judge, calling it "hallucinatory".
"I never approached Nir Hefetz about this, he never proposed to me anything about it, and you know what? I do not believe he raised the possibility with anyone," Netanyahu said.
In the other case revealed on Tuesday, police said they had arrested Hefetz and another Netanyahu confidant, Shlomo Filber, who once ran the Communications Ministry over allegations of corruption involving the telecoms firm Bezeq.
Bezeq's main shareholder, Shaul Elovitch, was also arrested, along with his wife and son, and Bezeq's CEO Stella Handler. Elovitch is a family friend of the Netanyahus. The arrests took place on Sunday but were not disclosed for two days under standard Israeli procedure.
Police suspect Bezeq received regulatory benefits in return for providing favourable media coverage of Netanyahu on Walla, a news website that is controlled by Elovitch's holding company Eurocom.
Elovitch has denied any wrongdoing, as have his wife and son, and Bezeq CEO Handler, a Eurocom spokeswoman said. Filber's lawyer declined to comment.
Netanyahu is not a suspect in that case but Israeli media said he was likely to be questioned soon.
Last week, police recommended Netanyahu be indicted in two of three investigations against him.
Police have dubbed the three corruption cases as 1,000, 2,000 and 3,000.
The first case, 1,000, revolves around gifts from wealthy supporters including Australian billionaire James Packer.
The second case is concerned with suspicions that Netanyahu discussed a secret deal to help scale down the circulation of Israel Hayom newspaper in exchange for more favorable coverage in rival publication Yediot Aharonot.
The third case centers on fraudulent purchases of German submarines in a $1.5bn deal.